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Plausible values and Plausibility Range 1

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Prevalence of FSWs in some west African Countries 2 0.1% 4.3%

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Plausible values In west African countries, prevalence of FSWs ranged 0.1% to 4.3%. Suppose you implement a study in another country in this region, and get a prevalence of 10%. How plausible this figure is? Did you implement the study in high risk locations? What are the potential biases in your study (selection of respondents, data collection, …)? What are the main cultural and socioeconomic differences between this country and others? 3

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Comparison of prevalence across risk zones Suppose, we have stratified the country into low, intermediate and high risk zones. We have selected one province from each zone. The prevalence in low zone was higher than that of high zone. How plausible it is? Have you implemented standard approach in all provinces? Have you trained the interviewers of the study? Have you used the right criteria to define the risk zones? 4

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Point Estimate vs. plausible range One of the aims of statistics is estimating population parameters from sample statistics For example, in a randomly selected sample of prisoners, 25 out of 200 ones reports sharing of injection equipment Thus in the sample, 12.5% of the prisoners share injection equipments This value of 12.5% is called a point estimate of the population proportion 5

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Sampling Variation Point estimate is a value derived from one randomly selected sample We use it as the best guess for the population parameter What would happen if we select another random sample? If you repeat the mapping or the NSU survey, do you expect to get the same estimates? What is the impact of respondents, locations, and time … 6

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Construction of a Range It is preferred to report a range of possible values, instead of a single point estimate It is conventional to create 95% range which means that 95% of the time constructed range contains the true value of the parameter of interest The width of the range provides some idea about uncertainty of the unknown parameter A very wide interval may indicate that more data should be collected before anything very definite can be said about the parameter. 7

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Advantages of Reporting a Range A smaller confidence interval is always more desirable than a larger one because it shows that the population parameter can be estimated more accurately Point estimation gives us a particular value as an estimate of the population parameter Interval estimation gives us a range of values which is likely to contain the population parameter 8

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Interpretation of Range The upper and lower bounds of the interval give us information on how big or small the true parameter might be Wide range indicates great uncertainty in the true value of the parameter 9

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Different Names for Range Statistical terminology – Confidence Interval – Uncertainty Limit – Credibility Interval Non-statistical terminology (in this course) – Plausibility Range 10

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How to Construct Statistical Ranges? Standard Formulas Based on Normal approximation Monte Carlo Bootstrapping – Works based on resampling with replacement from the original sample – Estimation of parameter of interest in each sample – Use of 2.5 and 97.5 percentiles at lower and upper bounds 11

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Application of available formulas To estimate number of IDUs, capture-recapture study has been implemented: 12

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How to Construct Non-Statistical Ranges? In the following slides we introduce some approaches followed by other researchers In addition, we introduce some other approaches based on common sense 17

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Other Countries Experience Indonesia applied the following formula: – x(i) = estimated size in district (i) – = mean of district sizes – n =number of districts Probably they used this statistics as SE and applied normal approximation theory 18

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Ad Hoc Methods (1) In other study, time-varying parameters were assigned uncertainty bounds in the model up to ± 50% of the best parameter estimates. Parameter estimates:50000 20%*50000=10000 uncertainty bounds: 50000 ± 10000 (40000, 60000) 19

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Ad Hoc Methods (2) Ask respondents to provide a range, instead of a single value For example, in NSU, ask respondents to count minimum and maximum of FSWs they know Analysis lower bound data should provide the lower bound of the plausibility range Analyzing the upper bound data should provide the upper bound of the plausibility range 20

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Chapter 19 Confidence intervals for proportions

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